Free products of von Neumann algebras

Ching, Wai Mee

doi:10.1090/S0002-9947-1973-0326405-3

Free products of von Neumann algebras

Author: Wai Mee Ching
Journal: Trans. Amer. Math. Soc. 178 (1973), 147-163
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9947-1973-0326405-3
MathSciNet review: 0326405
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Abstract: A new method of constructing factors of type ${\text {II}_1}$, called free product, is introduced. It is a generalization of the group construction of factors of type ${\text {II}_1}$ when the given group is a free product of two groups. If ${A_1}$ and ${A_2}$ are two von Neumann algebras with separating cyclic trace vectors and ortho-unitary bases, then the free product ${A_1} \ast {A_2}$ of ${A_1}$ and ${A_2}$ is a factor of type ${\text {II}_1}$ without property $\Gamma$.

H. Behncke, Automorphisms of $\mathcal {A}({\Phi _2})$, notes.

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